Uses formulae from linear wavy theory. More...
#include <velocity_potential.hh>
Public Member Functions | |
| void | solve (const Grid< T, 4 > &grid_tzxy, const Array< T, 3 > &wavy_surface, Array< T, 4 > &velocity_potential) override |
| Computes velocity potential \(\phi\). More... | |
| void | window_function (const Grid< T, 2 > &wngrid, const T z, Array2< T > &result) |
| Computes window (first) function \(\mathcal{W}\). More... | |
| template<> | |
| void | window_function (const Grid< T, 2 > &wngrid, const T z, Array2< T > &result) |
| template<> | |
| void | solve (const Grid< T, 4 > &grid_tzxy, const Array< T, 3 > &zeta, Array< T, 4 > &phi) |
 Public Member Functions inherited from vtb::core::Linear_velocity_potential_solver_base< T > | |
| void | second_function (const Grid< T, 4 > &grid_tzxy, const Array3< T > &wavy_surface, Array3< C > &result) |
| Computes second function. More... | |
| Public Member Functions inherited from vtb::core::Velocity_potential_solver< T, 3 > | |
| T | depth () const noexcept |
| Get water depth. | |
| void | depth (T rhs) |
| Set water depth. | |
| void | wave_number_grid (const Grid< T, 2 > &rhs) |
| const Grid< T, 2 > & | wave_number_grid () const |
| void | assumptions (Assumptions rhs) |
| const Assumptions & | assumptions () const |
| virtual void | solve (const Grid< T, N+1 > &grid_tzxy, const Array< T, N > &wavy_surface, Array< T, N+1 > &velocity_potential)=0 |
| Calculate velocity potential for each grid point. More... | |
| void | operator() (const Grid< T, 4 > &grid_tzxy, const Array< T, 3 > &wavy_surface, Array< T, 4 > &velocity_potential) |
Detailed Description
template<class T, Policy P>
class vtb::core::Linear_velocity_potential_solver< T, P >
Uses formulae from linear wavy theory.
- Date
- 2018-08-14
Definition at line 151 of file velocity_potential.hh.
Member Function Documentation
◆ solve()
|
override |
Computes velocity potential \(\phi\).
- Date
- 2018-08-14
- See also
- window_function
- second_function
The integration is implemented using FFT and is done over wave number range which is computed directly from the wavy surface.The main formula for velocity potential is
\[ \phi(x,y,z;t) = \mathcal{F}^{-1}_{x,y}\left\{ \mathcal{W}(u,v;z) \cdot \mathcal{F}_{u,v}\left\{\mathcal{S}(x,y;t)\right\} \right\}, \]
where \(\mathcal{W}\) is window function and \(\mathcal{S}\) is second function. For details see documentation of the corresponding methods.
◆ window_function()
| void vtb::core::Linear_velocity_potential_solver< T, P >::window_function | ( | const Grid< T, 2 > & | wngrid, |
| const T | z, | ||
| Array2< T > & | result | ||
| ) |
Computes window (first) function \(\mathcal{W}\).
- Date
- 2018-08-14
- For infinite depth the formula is
\[ \mathcal{W}(\vec{k}) = \frac{\exp\left(|\vec{k}|\right)}{|\vec{k}|}. \]
- For finite depth the formula is
\[ \mathcal{W}(\vec{k}) = \frac {\cosh\left(|\vec{k}|(z+h)\right)} {|\vec{k}|\cosh\left(|\vec{k}|h\right)}. \]
